Geological formations forming a reservoir for the accumulation of hydrocarbons in the subsurface of the earth contain a network of interconnected paths in which fluids are disposed that may ingress or egress from the reservoir. To determine the behavior of the fluids in this network, knowledge of both the porosity and permeability of the geological formations is desired. From this information, efficient development and management of hydrocarbon reservoirs may be achieved. For example, the resistivity of geological formations is a function of both porosity and permeability. Considering that hydrocarbons are electrically insulative and most water contain salts, which are highly conductive, resistivity measurements are a valuable tool in determining the presence of hydrocarbon reservoir in the formations.
To that end, there have been many prior art attempts to model geological formations. In two articles, “Crosshole Electromagnetic Tomography: A New Technology for Oil Field Characterization,” The Leading Edge, March 1995, by Wilt et al. and “Crosshole Electromagnetic Tomography: System Design Considerations and Field Results,” Society of Exploration Geophysics, Vol. 60, No. 3 1995, by Wilt et al., measurement of geological formation resistivity is described employing a low frequency electromagnetic system.
FIG. 1 shows typical equipment used in the measurement of geological formation 10 resistivity between two drill holes 12a and 12b using electromagnetic induction. A transmitter T is located in one borehole, while a receiver R is placed in another borehole. The transmitter T typically consists of a coil (not shown) having a multi-turn loop (which consists of NT turns of wire) wrapped around a magnetically permeable core (mu-metal or ferrite) with a cross section, AT. The transmitter T may further comprise a capacitor (not shown) for tuning the frequency of the coil. When an alternating current, IT, at a frequency of f0 Hz passes through this multi-turn loop, a time varying magnetic moment, MT, is produced in the transmitter T. This magnetic moment is defined as follows:MT=NTITAT  (1)
The magnetic moment MT can be detected by the receiver R as a magnetic field, BR. The transmitter T, receiver R, or both are typically disposed in boreholes (e.g., 12a and 12b) in the earth formation 10. In this case, the detected magnetic field, BR, is proportional to the magnetic moment of the transmitter, MT, and to a geological factor, kf, and a geometric factor b. In a rectangular coordinate system with the dipole moment MT in the x direction the field of a dc dipole ( or a low frequency dipole in free space is given by;
                              B          _                =                                                            μ                0                            ⁢                              M                T                                                    4              ⁢                                                          ⁢              π              ⁢                                                          ⁢                              r                3                                              [                                                                      x                  2                                                  r                  2                                            ⁢                                                u                  _                                x                                      +                                                            x                  ⁢                                                                          ⁢                  y                                                  r                  2                                            ⁢                                                u                  _                                y                                      +                                                            y                  ⁢                                                                          ⁢                  z                                                  r                  2                                            ⁢                                                u                  _                                z                                              ]                                    (                  2          ⁢          a                )            where the ū are unit vectors in the x, y, and z directions. As the frequency increases when the dipole is in a conductive formation the above magnetic response is modified by the induced currents in the formation by a factor which is called here the formation factor kf. In a short form, the response may be written asBR=bkfMT  (2b)
The geological factor, kf, is a function of the electrical conductivity distribution of the geological formation between the transmitter and the receiver. The factor b is a function of the spatial location and orientation of the field component of the magnetic field, BR, with respect to the magnetic moment of the transmitter, MT.
The receiver R typically includes one or more antennas (not shown). Each antenna includes a multi-turn loop of wire wound around a core of magnetically permeable metal or ferrite. The changing magnetic field sensed by the receiver R creates an induced voltage in the receiver coil (not shown). This induced voltage (VR) is a function of the detected magnetic field (BR), the frequency (f0), the number of turns (NR) of wire in the receiver coil, the effective cross-sectional area of the coil (AR), and the effective permeability (ρR) of the coil. Thus, VR can be defined as follows:VR=πf0BRNRARρR  (3)
While f0 and NR are known, the product, AR ρR, is difficult to calculate. In practice, these constants may be grouped together as kR and equation (3) may be simplified as:VR=kRBR  (4)where kR=πf0NRARρR.
Thus, instead of determining the product AR ρR, it is more convenient to determine kR according to the following procedures. First, the receiver coil is calibrated in a known field, at a known frequency. Then, the exact value for kR is derived from the magnetic field (BR) and the measured voltage (VR) according to the following equation:kR=BR/VR  (5)
When this system is placed in a conducting geological formation, the time-varying magnetic field, BR, which is produced by the transmitter magnetic moment MT, produces a voltage in the geological formation, which in turn drives a current therein, L1. The current, L1, is proportional to the conductivity of the geological formation and is generally concentric about the longitudinal axis of the borehole. The magnetic field proximate to the borehole results from a free space field, called the primary magnetic field, while the field resulting from current L1 is called the secondary magnetic field.
The current, L1, is typically out of phase with respect to the transmitter current, IT. At very low frequencies, where the inductive reactance is small, the current, L1, is proportional to dB/dt and is 90° out of phase with respect to IT. As the frequency increases, the inductive reactance increases and the phase of the induced current, L1, increases to greater than 90°. The secondary magnetic field induced by current L1 also has a phase shift relative to the induced current L1 and so the total magnetic field as detected by receiver R is complex.
The complex magnetic field detected by receiver R may be separated into two components: a real component, BR, which is in-phase with the transmitter current, IT, and an imaginary (or quadrature) component, BI, which is phase-shifted by 90°. The values of the real component, BR, and the quadrature component, BI, of the magnetic field at a given frequency and geometrical configuration uniquely specify the electrical resistivity of a homogeneous formation pierced by the drill holes. In an inhomogeneous geological formation, however, the complex field is measured at a succession of points along the longitudinal axis of the receiver borehole for each of a succession of transmitter locations. The multiplicity of measurements thus obtained can then be used to determine the inhomogeneous resistivity distribution between the holes.
In both cases, i.e., measuring homogeneous geological formation resistivity or measuring inhomogeneous geological formation resistivity, the measurements are typically made before extraction of hydrocarbons takes place. This is because the boreholes typically are cased with conductive liners (e.g., metallic casing; see 16a and 16b in FIG. 1) in order to preserve the physical integrity of the borehole during hydrocarbon extraction. The conductive tubular liners interfere with resistivity measurements and are difficult and costly to remove from the borehole once they are installed. As a result, prior art systems such as that shown in FIG. 1 are not suitable for analyzing hydrocarbon reservoirs once extraction of the hydrocarbons begins.
The problems presented by conductive liners (16a and 16b in FIG. 1) are described by Augustin et al., in “A Theoretical Study of Surface-to-Borehole Electromagnetic Logging in Cased Holes,” Geophysics, Vol. 54, No. 1 (1989); Uchida et al., in “Effect of a Steel Casing on Crosshole EM Measurements,” SEG Annual Meeting, Texas (1991); and Wu et al., in “Influence of Steel Casing on Electromagnetic Signals,” Geophysics, Vol. 59, No. 3 (1994). These prior art references show that coupling between a transmitter and a conductive liner is independent of the surrounding geological formation conductivity for a wide range of practical formation resistivities encountered in the field. The references show further that the magnetic field produced inside the conductive liner at a distance of a few meters or less from the transmitter depends only on the conductive liner properties and not on the formation properties.
The net or effective moment, Meff, of a transmitter inside a conductive liner is dictated by the inductive coupling between the transmitter and the conductive liner. Physically, the resistivity of the conductive liner is very low and the inductance relatively high. This property results in a current of almost the same magnitude as that of the transmitter current being induced in the conductive liner. Lenz's Law predicts that the magnetic field generated by this induced current in the conductive liner will oppose the time-varying magnetic field produced by the transmitter current. Thus, the magnetic field generated by the transmitter is mostly cancelled out by the magnetic field generated by the conductive liner. As a result, the magnetic field external to the conductive liner is greatly reduced, and its magnitude is proportional to the difference in currents in the transmitter and the conductive liner. In effect, the conductive liner “shields” the transmitter from any receiver positioned outside of the conductive liner. This is sometimes referred to herein as the “casing effect” on the measurement of the external magnetic field. The effective moment, the moment seen by a receiver outside the casing, is conveniently expressed by:Meff=kcMT  (6)where kc is the casing attenuation factor.
An analogous situation is present with respect to a receiver if it is surrounded by a conductive liner, and the situation is exacerbated if both the transmitter and the receiver are surrounded by conductive liners.
To overcome the shielding problem (the “casing effect” or “casing attenuation effects”), various techniques have been suggested. For example, U.S. Pat. No. 5,646,533, entitled “Induction Measurement in the Presence of Metallic, Magnetic Walls” and issued to Locatelli, et al., discloses a method of magnetically saturating the metallic wall to overcome this problem. Alternatively, gapped casing has been used to achieve a similar effect. Another approach is to determine the conductive liner properties (e.g., radius, thickness, conductivity, and permeability) and then compensate for these properties. However, the correction needed to compensate for the conductive liner properties may be several orders of magnitude larger than the magnetic field sensed by the receiver outside the casing. Any inaccurate correction for the conductive liner properties would have an enormous impact on the accuracy of the “corrected field.” Furthermore, conductive liners often are not homogeneous (e.g., due to variation in thickness, corrosion, or rust formation); such variations may further compromise the accuracy of the “corrected field.”
Before providing more detailed description of this preferred or improved method, it may be helpful to elaborate further on crosshole electromagnetic surveys in general.
In addition to frequency, other important survey parameters include the length of the data profiles and the spacing between receiver points. These parameters determine the duration of the field survey as well as the resolution of the images. Ideally, individual data profiles should be twice as long as the borehole separation and the spacing between receiver data points should be about five percent (5%) of the well separation. For example, where the boreholes are spaced 200 meters apart, the profiles should be 400 meters long (along the axial length of the borehole) with a receiver 24, FIG. 2, spaced every 10 meters in each of the boreholes. Note that data are collected continuously as the transmitter moves in one of the boreholes, so the physical spacing between transmitter readings is much closer than spacing between the transmitter 20 and receiver 24.
Sometimes the imaging target lies within a restricted depth interval. For example, a particular oil sand undergoing water flooding. In this case the tomography can be substantially focused on this interval and the profile length reduced. It is recommended that a profile length equal to the distance between wells and a receiver spacing of five percent (5%) of the borehole spacing in the region of interest, but ten (10%) above or below these depths. The resulting image will provide good detail in the region of interest but less above or below.
Additionally, there are often physical restrictions on a survey. For example, imaging boreholes are frequently completed to the depth of the primary hydrocarbon bearing zone. It is useful, however, to extend the measurements to below this interval, but this is not possible if existing wells are utilized. The output of images taken under these less than ideal conditions is not always predictable. Usually the resolution is somewhat reduced as compared to full coverage data, but often the data are sufficient for resolving large-scale structures. In addition, these data are often still quite valuable for process monitoring applications, such as in water or steam floods.
During operation, receiver 24 is positioned at various fixed depths within the borehole 12b, while transmitter 20 is pulled up continuously at a constant rate, vice versa. Therefore, for every position of receiver 24, there are measurements made at a plurality of positions of transmitter 20, defining a run of data. A plurality of runs of data is taken, with receiver 24 positions at different depths for each run. In this manner, one complete set of tomography data within the depth range of interest is achieved. Usually, the intervals between different positions of receiver 24 are about 5% of the distance between the boreholes. Receiver 24 may be first moved by twice this interval at a plurality of positions. After the desired region has been measured, receiver 24 is moved back to acquire the data at points equal-distance from adjacent positions of the aforementioned plurality of positions.
During data acquisition, procedures should be undertaken to ensure high quality measurements. To that end, initial tests may include the magnetic fields generated and sensed by system 19 with both transmitter 20 and receiver 24 suspended in the air above the boreholes. This facilitates determining the primary magnetic field without the effect of the earth.
In addition, a linearity test may be conducted after transmitter 20 and receiver 24 have been lowered in their respective borehole. A measurement at the standard operating voltage is made, followed by a second measurement at a lower voltage. The ratio of the resultant magnetic fields to the transmitter flux should be within about ten percent for each voltage level. After passing the linearity and primary field tests, normal logging operations may commence. It is preferred that the initial two logging runs be reserved for a repeatability test. These back-to-back logs should agree to within about one percent in amplitude and about one degree in phase for logging to proceed. “Warm” transmitter 20 and receiver 24 response should be within the one percent tolerance. Tests may also be performed during logging.
Tests may also be conducted on the measurements after the data collection is complete. One such test is referred to as a profile tie in which transmitter 20 is maintained at a fixed position near the top of the profile and sequentially moves receiver 24 to all of the depths it previously occupied during the analysis. A careful measurement is made at each depth of receiver 24. This procedure is then repeated for a second position of transmitter 20 within the borehole. The measurements made during the profile tie are used to tie the individual profiles together.
An additional test conducted on the measurements is referred to as a reciprocity test. This reciprocity test involves exchanging the positions of transmitter 20 and receiver 24. It is preferred to measure reciprocity by establishing at least three positions at known depths, in the boreholes: shallow, intermediate and deep. Measurements are then made with transmitter 20 and receiver 24 in each position in each borehole. This involves measuring the data in the present logging position and then interchanging the transmitter 20 and the receiver 24 and making the measurements a second time. These measurements serve to test the depth control of system 19, as well as the stability and linearity of the signals propagating between transmitter 20 and receiver 24.
Although the foregoing has been described with only borehole 12a being lined with a conductive liner 16a, in practice either borehole 12a or 12b, or both may be lined. An analogous technique may be employed to determine the reduction in the magnetic field sensed by receiver 24 by conductive liner 16b. As before, the incident magnetic field induces a current in conductive liner 16b, which acts according to Lenz's law to reduce the magnetic field inside the borehole 12b. That is, conductive liner 16b shields receiver 24 from the incident magnetic field in a way similar to how conductive liner 16a shields and attenuates the magnetic field generated by transmitter 20.